Over the last decade, the number of macromolecular structures determined by X-ray diffraction has increased dramatically, driven by revolutions in a number of supporting technologies [1-3]. An absolutely essential part of the process, crystallization, is still not fully understood (reviewed in [4, 5]).
Two theoretical innovations, incomplete factorial analysis [6] and sparse matrix screening [7], introduced the idea of analyzing combinations of independent factors that affect crystallization. Widespread success with the latter suggested that, once at the precipitation point, having the proper combination of factors is more important than subtle variation in the concentration of any single factor. Still, success with sparse matrix screening is intimately tied to the choice of independent factors upon which the matrix is based. In both the original incomplete factorial and sparse matrix analyses [6, 7], the precipitating agent was treated as a single independent variable. But precipitating agents can function by altering the activity coefficient of water (salts) [8], by altering the dielectric constant of the solvating medium (organic solvents) [9] or by increasing molecular crowding (high molecular weight polymers like polyethylene glycol [PEG]) [10, 11]. The notion of precipitant combinations has been speculated upon (for example by Carter in [12]), but never experimentally developed or tested.